CN116184368B - Gaussian-Markov-based airborne radar placement error interpolation correction method - Google Patents

Gaussian-Markov-based airborne radar placement error interpolation correction method Download PDF

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CN116184368B
CN116184368B CN202310449332.7A CN202310449332A CN116184368B CN 116184368 B CN116184368 B CN 116184368B CN 202310449332 A CN202310449332 A CN 202310449332A CN 116184368 B CN116184368 B CN 116184368B
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刘杰
柳泽政
陈万前
吕婧
杜立彬
孟祥谦
林欣泽
黄鸿志
李雨鑫
江国辉
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Abstract

The invention discloses a Gaussian-Markov-based airborne radar placement error interpolation correction method, which belongs to the technical field of laser radar measurement and is used for correcting the placement error of an airborne radar and comprises the following steps: establishing and solving a plane equation with robust property, and removing abnormal points and rough difference points in the point cloud surface; and (3) carrying out setting error adjustment calculation based on plane constraint, taking a setting angle error as an unknown parameter, converting a laser scanning coordinate system into an inertial platform reference coordinate system, combining an observed value in a geometric positioning model of an airborne laser radar system, establishing a calibration model, carrying out parameter calculation by utilizing a conditional adjustment with parameters, carrying out the same calculation by taking the setting eccentric distance error as the parameters, obtaining the setting error, and finally carrying out step adjustment calculation.

Description

Gaussian-Markov-based airborne radar placement error interpolation correction method
Technical Field
The invention discloses a Gaussian-Markov-based airborne radar placement error interpolation correction method, and belongs to the technical field of laser radar measurement.
Background
The positioning error is the largest error source in the system error of the domestic airborne laser radar, wherein the influence of positioning accuracy of the positioning angle error increases with the increase of the navigational altitude, namely, the positioning angle error between the INS coordinate reference frame and the laser scanning reference system is the largest system error source in the airborne laser radar. Empirically, these placement angle errors are typically 0.1-0.3 °, and the effect of placement angle errors on the ground laser foot coordinates is also dependent on the altitude of the flight and the magnitude of the scan angle.
Compared with aerial photogrammetry, the data result of the domestic airborne laser radar is point cloud, has irregularity and discreteness, can not ensure that measurement data just exist at characteristic points, does not exist in the true sense of the concept of homonymous points, and often needs to convert connection relations. And matching the characteristic points and the lines, calibrating the placement errors as unknown parameters by adopting a method of adjustment and least square, establishing a certain model for fitting and interpolation, and obtaining the higher the accuracy of the characteristic points as the density of the point cloud is higher.
Disclosure of Invention
The invention aims to provide a Gaussian-Markov airborne radar placement error interpolation correction method, which aims to solve the problem that the airborne radar placement error correction is difficult in the prior art.
The Gaussian-Markov-based airborne radar placement error interpolation correction method comprises the following steps:
s1, establishing and solving a plane equation with robust property, and removing abnormal points and rough difference points in a point cloud surface;
s2, carrying out setting error adjustment calculation based on plane constraint;
taking the placement angle error as an unknown parameter, converting a laser scanning coordinate system into an inertial platform reference coordinate system, combining an observed value in a geometric positioning model of an airborne laser radar system, establishing a calibration model, carrying out parameter calculation by utilizing a conditional variance with parameters, and then taking the placement eccentricity error as a parameter, and carrying out the same calculation to obtain the placement error;
s3, calculating step-by-step adjustment.
Establishing and solving a plane equation with robust properties includes:
s1.1, setting a plane equation to be fitted as follows:
Figure SMS_1
（1）；
where a, b, c, d is an equation parameter, x, y, z represent the coordinates of a point;
the normal vector formed by the plane equation is considered as a unit normal vector, namely:
Figure SMS_2
（2）；
the distance from any point in space to the plane
Figure SMS_3
Expressed as:
Figure SMS_4
（3）；
wherein x is i 、y i 、z i Coordinates representing an arbitrary point;
s1.2, setting the best fit plane constraint condition
Figure SMS_5
The method comprises the following steps:
Figure SMS_6
（4）；
construction of Lagrangian auxiliary function
Figure SMS_7
：
Figure SMS_8
（5）；
In the method, in the process of the invention,
Figure SMS_9
is a parameter of the Lagrangian auxiliary function;
and d, obtaining a deviation, namely obtaining:
Figure SMS_10
（6）；
s1.3. rewriting formula (6) to:
Figure SMS_11
（7）；
wherein,,
Figure SMS_12
、/>
Figure SMS_13
、/>
Figure SMS_14
respectively x i 、y i 、z i Mean value of->
Figure SMS_15
；
Derivative a, b and c and let the derivative be 0, and obtaining:
Figure SMS_16
（8）；
in the method, in the process of the invention,
Figure SMS_17
the eccentricity error is set for each reference target point of the standard surface;
s1.4, constructing a eigenvalue equation:
Figure SMS_18
（9）；
and (3) obtaining the minimum eigenvalues of the coefficient matrix of the eigenvalue equation and the eigenvectors corresponding to the minimum eigenvalues, namely obtaining a, b and c, and taking the obtained a, b and c into a formula (3), thus obtaining d.
Removing abnormal points and rough difference points in the point cloud surface comprises the following steps:
B1.1. calculating the distance between all points and the fitting plane according to a, b, c, d obtained in the step S1;
B1.2. calculating an error according to (10)
Figure SMS_19
：
Figure SMS_20
（10）；
Wherein n is the number of points,
Figure SMS_21
mean value of d, +.>
Figure SMS_22
；
B1.3. When meeting the requirements
Figure SMS_23
When (I)>
Figure SMS_24
Corresponding points are reserved, otherwise, the points are removed;
B1.4. recalculating plane parameters a, b, c, d by using the removed point cloud;
B1.5. repeating S2.1-S2.4 until all points are satisfied
Figure SMS_25
；
B1.5. And (3) taking the a, b and c obtained in the step S2.5 into a formula (3), and obtaining d, wherein the best plane fitting equation is obtained.
Converting the laser scanning coordinate system to the inertial platform reference coordinate system includes:
the observations of the S2.1. error equation are symbolized as
Figure SMS_26
：/>
Figure SMS_27
；
Wherein:
Figure SMS_28
the scanning electrode diameter is; />
Figure SMS_29
Is the scan angle; />
Figure SMS_30
Is a roll angle; />
Figure SMS_31
Is a pitch angle; />
Figure SMS_32
Is the deflection angle; />
Figure SMS_33
Is the coordinates of the reference center in the WGS84 coordinate system;
the unknown parameters of the error equation are symbolized as
Figure SMS_34
：/>
Figure SMS_35
；
Wherein:
Figure SMS_36
for setting angle error->
Figure SMS_37
To accommodate eccentricity errors;
s2.2, converting the laser scanning coordinate system into an inertial platform reference coordinate system, wherein the method comprises the following steps of:
defining pitch angle inverse from laser scanning coordinate system to carrier coordinate system to inertial platform reference coordinate system
Figure SMS_38
Rotation is positive, side roll angle is reverse +.>
Figure SMS_39
Rotation is positive, course angle is reverse +.>
Figure SMS_40
Rotation is positive and +.>
Figure SMS_41
For the coordinates of the origin of the laser scanning coordinate system in the inertial platform reference coordinate system, it is assumed that the setting angles are positive, +.>
Figure SMS_42
Is the coordinate axis of the laser scanning coordinate system, +.>
Figure SMS_43
Is a coordinate axis of an inertial platform reference coordinate system;
s2.2.1. first winding
Figure SMS_44
Rotating Deltaroll, deltaroll being roll angle, & lt->
Figure SMS_45
Become->
Figure SMS_46
：
Figure SMS_47
（11）；
In the method, in the process of the invention,
Figure SMS_48
is +.>
Figure SMS_49
；
S2.2.2. winding
Figure SMS_50
Rotating Δpitch, which is pitch angle, and +.>
Figure SMS_51
Become->
Figure SMS_52
：
Figure SMS_53
（12）；
In the method, in the process of the invention,
Figure SMS_54
for +.>
Figure SMS_55
；
S2.2.3. winding
Figure SMS_56
Rotation delta yaw, delta yaw is the declination angle, +.>
Figure SMS_57
Become->
Figure SMS_58
：
Figure SMS_59
（13）；
In the method, in the process of the invention,
Figure SMS_60
is +.>
Figure SMS_61
；
S3.2.4. to sum up, formulae (11), (12), (13) can be obtained:
Figure SMS_62
（14）；
in the method, in the process of the invention,
Figure SMS_63
to simplify the matrix +.>
Figure SMS_64
。
After converting the laser scanning coordinate system into the inertial platform reference coordinate system, the following steps are executed:
s2.3 plane equation of standard surface corresponding to calibration surface point cloud
Figure SMS_65
The following are provided:
Figure SMS_66
；
wherein,,
Figure SMS_67
；
Figure SMS_68
coordinate matrix for standard surface reference target point +.>
Figure SMS_69
A rotation error correction conversion matrix is arranged for the plane equation,
Figure SMS_70
setting an eccentricity error correction conversion matrix for plane equation, < >>
Figure SMS_71
A coordinate matrix of the standard plane reference center in a WGS84 coordinate system;
Figure SMS_72
。
s3:
taking the setting angle as a parameter, taking the translation amount as a known value, listing an equation for solving, and applying a Gaussian-Markov model by using a global least square method, wherein the solving principle comprises the following steps:
the global least squares method applies a gaussian-markov model as:
Figure SMS_73
；
in the middle of
Figure SMS_74
For placement error->
Figure SMS_75
For the coefficient matrix of n rows and m columns to be measured and calculated, < >>
Figure SMS_76
For the error matrix existing in A, Y is the error vector to be calculated, and B is the error estimation parameter.
The step-by-step adjustment calculation step comprises the following steps:
s3.1, establishing a global least square method and applying a Gaussian-Markov model;
s3.2. pair amplification matrix
Figure SMS_77
Singular value decomposition is performed:
Figure SMS_78
；
wherein the method comprises the steps of
Figure SMS_80
，/>
Figure SMS_81
，/>
Figure SMS_82
、/>
Figure SMS_83
、/>
Figure SMS_84
、/>
Figure SMS_85
、/>
Figure SMS_86
、/>
Figure SMS_79
All are decomposed submatrices decomposed by singular values of the matrix;
s3.3. If
Figure SMS_87
Non-singular, get->
Figure SMS_88
，/>
Figure SMS_89
Is a linear regression of a sign, i.e. a straight line is made for a given number of points and the error minimum value of the points;
s3.4. precision assessment
Figure SMS_90
，/>
Figure SMS_91
I.e. standard deviation of placement error>
Figure SMS_92
In the range of 0.03-0.1, the accuracy of the placement error is reliable.
Compared with the prior art, the invention has the following beneficial effects: calibration of the placement error is necessary in order to obtain the exact coordinates of the laser foot points. Compared with aerial photogrammetry, the data result of the airborne laser radar is point cloud, has irregularity and discreteness, can not ensure that measurement data just exist at characteristic points, does not exist in the true sense of the concept of homonymy points, and needs to carry out coordinate conversion on connection relations. And matching the characteristic points and the lines, measuring and calculating the placement error serving as an unknown parameter by adopting a global least square method, establishing a model and carrying out interpolation calculation, so that the placement error is accurately inverted. The point cloud data has rough difference points, so that the fitting plane model is required to have strong anti-difference property, the plane equation with the anti-difference property is solved, and the Gaussian-Markov model well solves the problem, and the obtained placement angle error is more accurate because the standard surface reference target point used by the Gaussian-Markov model has strong anti-difference property.
Drawings
Fig. 1 is a technical flow chart of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions in the present invention will be clearly and completely described below, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The Gaussian-Markov-based airborne radar placement error interpolation correction method, as shown in FIG. 1, comprises the following steps:
s1, establishing and solving a plane equation with robust property, and removing abnormal points and rough difference points in a point cloud surface;
s2, carrying out setting error adjustment calculation based on plane constraint;
taking the placement angle error as an unknown parameter, converting a laser scanning coordinate system into an inertial platform reference coordinate system, combining an observed value in a geometric positioning model of an airborne laser radar system, establishing a calibration model, carrying out parameter calculation by utilizing a conditional variance with parameters, and then taking the placement eccentricity error as a parameter, and carrying out the same calculation to obtain the placement error;
s3, calculating step-by-step adjustment.
Establishing and solving a plane equation with robust properties includes:
s1.1, setting a plane equation to be fitted as follows:
Figure SMS_93
（1）；
where a, b, c, d is an equation parameter, x, y, z represent the coordinates of a point;
the normal vector formed by the plane equation is considered as a unit normal vector, namely:
Figure SMS_94
（2）；
the distance from any point in space to the plane
Figure SMS_95
Expressed as:
Figure SMS_96
（3）；
wherein x is i 、y i 、z i Coordinates representing an arbitrary point;
s1.2, setting the best fit plane constraint condition
Figure SMS_97
The method comprises the following steps:
Figure SMS_98
（4）；
construction of Lagrangian auxiliary function
Figure SMS_99
：
Figure SMS_100
（5）；
In the method, in the process of the invention,
Figure SMS_101
is a parameter of the Lagrangian auxiliary function;
and d, obtaining a deviation, namely obtaining:
Figure SMS_102
（6）；
s1.3. rewriting formula (6) to:
Figure SMS_103
（7）；
wherein,,
Figure SMS_104
、/>
Figure SMS_105
、/>
Figure SMS_106
respectively x i 、y i 、z i Mean value of->
Figure SMS_107
；
Derivative a, b and c and let the derivative be 0, and obtaining:
Figure SMS_108
（8）；
in the method, in the process of the invention,
Figure SMS_109
the eccentricity error is set for each reference target point of the standard surface;
s1.4, constructing a eigenvalue equation:
Figure SMS_110
（9）；
and (3) obtaining the minimum eigenvalues of the coefficient matrix of the eigenvalue equation and the eigenvectors corresponding to the minimum eigenvalues, namely obtaining a, b and c, and taking the obtained a, b and c into a formula (3), thus obtaining d.
Removing abnormal points and rough difference points in the point cloud surface comprises the following steps:
B1.1. calculating the distance between all points and the fitting plane according to a, b, c, d obtained in the step S1;
B1.2. calculating an error according to (10)
Figure SMS_111
：
Figure SMS_112
（10）；
Wherein n is the number of points,
Figure SMS_113
mean value of d, +.>
Figure SMS_114
；
B1.3. When meeting the requirements
Figure SMS_115
When (I)>
Figure SMS_116
Corresponding points are reserved, otherwise, the points are removed;
B1.4. recalculating plane parameters a, b, c, d by using the removed point cloud;
B1.5. repeating S2.1-S2.4 until all points are satisfied
Figure SMS_117
；
B1.5. And (3) taking the a, b and c obtained in the step S2.5 into a formula (3), and obtaining d, wherein the best plane fitting equation is obtained.
Converting the laser scanning coordinate system to the inertial platform reference coordinate system includes:
the observations of the S2.1. error equation are symbolized as
Figure SMS_118
：/>
Figure SMS_119
；
Wherein:
Figure SMS_120
the scanning electrode diameter is; />
Figure SMS_121
Is the scan angle; />
Figure SMS_122
Is a roll angle; />
Figure SMS_123
Is a pitch angle; />
Figure SMS_124
Is the deflection angle; />
Figure SMS_125
Is the coordinates of the reference center in the WGS84 coordinate system;
the unknown parameters of the error equation are symbolized as
Figure SMS_126
：/>
Figure SMS_127
；
Wherein:
Figure SMS_128
for setting angle error->
Figure SMS_129
To accommodate eccentricity errors;
s2.2, converting the laser scanning coordinate system into an inertial platform reference coordinate system, wherein the method comprises the following steps of:
defining pitch angle inverse from laser scanning coordinate system to carrier coordinate system to inertial platform reference coordinate system
Figure SMS_130
Rotation is positive, side roll angle is reverse +.>
Figure SMS_131
Rotation is positive, course angle is reverse +.>
Figure SMS_132
Rotation is positive and +.>
Figure SMS_133
For the coordinates of the origin of the laser scanning coordinate system in the inertial platform reference coordinate system, it is assumed that the setting angles are positive, +.>
Figure SMS_134
Scanning coordinates for laserCoordinate axis of the system>
Figure SMS_135
Is a coordinate axis of an inertial platform reference coordinate system;
s2.2.1. first winding
Figure SMS_136
Rotating Deltaroll, deltaroll being roll angle, & lt->
Figure SMS_137
Become->
Figure SMS_138
：
Figure SMS_139
（11）；
In the method, in the process of the invention,
Figure SMS_140
is +.>
Figure SMS_141
；
S2.2.2. winding
Figure SMS_142
Rotating Δpitch, which is pitch angle, and +.>
Figure SMS_143
Become->
Figure SMS_144
：
Figure SMS_145
（12）；
In the method, in the process of the invention,
Figure SMS_146
for +.>
Figure SMS_147
；
S2.2.3. winding
Figure SMS_148
Rotation delta yaw, delta yaw is the declination angle, +.>
Figure SMS_149
Become->
Figure SMS_150
：
Figure SMS_151
（13）；
In the method, in the process of the invention,
Figure SMS_152
is +.>
Figure SMS_153
；
S3.2.4. to sum up, formulae (11), (12), (13) can be obtained:
Figure SMS_154
（14）；
in the method, in the process of the invention,
Figure SMS_155
to simplify the matrix +.>
Figure SMS_156
。
After converting the laser scanning coordinate system into the inertial platform reference coordinate system, the following steps are executed:
s2.3 plane equation of standard surface corresponding to calibration surface point cloud
Figure SMS_157
The following are provided:
Figure SMS_158
；
wherein,,
Figure SMS_159
；
Figure SMS_160
coordinate matrix for standard surface reference target point +.>
Figure SMS_161
A rotation error correction conversion matrix is arranged for the plane equation,
Figure SMS_162
setting an eccentricity error correction conversion matrix for plane equation, < >>
Figure SMS_163
A coordinate matrix of the standard plane reference center in a WGS84 coordinate system;
Figure SMS_164
。
s3:
taking the setting angle as a parameter, taking the translation amount as a known value, listing an equation for solving, and applying a Gaussian-Markov model by using a global least square method, wherein the solving principle comprises the following steps:
the global least squares method applies a gaussian-markov model as:
Figure SMS_165
；
in the middle of
Figure SMS_166
For placement error->
Figure SMS_167
For the coefficient matrix of n rows and m columns to be measured and calculated, < >>
Figure SMS_168
Is an error matrix existing in A, Y isAnd an error vector to be calculated, wherein B is an error estimation parameter.
The step-by-step adjustment calculation step comprises the following steps:
s3.1, establishing a global least square method and applying a Gaussian-Markov model;
s3.2. pair amplification matrix
Figure SMS_169
Singular value decomposition is performed:
Figure SMS_170
；
wherein the method comprises the steps of
Figure SMS_171
，/>
Figure SMS_173
，/>
Figure SMS_174
、/>
Figure SMS_175
、/>
Figure SMS_176
、/>
Figure SMS_177
、/>
Figure SMS_178
、/>
Figure SMS_172
All are decomposed submatrices decomposed by singular values of the matrix;
s3.3. If
Figure SMS_179
Non-singular, get->
Figure SMS_180
，/>
Figure SMS_181
Is a linear regression of a sign, i.e. a straight line is made for a given number of points and the error minimum value of the points;
s3.4. precision assessment
Figure SMS_182
，/>
Figure SMS_183
I.e. standard deviation of placement error>
Figure SMS_184
In the range of 0.03-0.1, the accuracy of the placement error is reliable.
The above embodiments are only for illustrating the technical aspects of the present invention, not for limiting the same, and although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may be modified or some or all of the technical features may be replaced with other technical solutions, which do not depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (3)

1. The method for interpolating and correcting the placement error of the airborne radar based on Gaussian-Markov is characterized by comprising the following steps:
s1, establishing and solving a plane equation with robust property, and removing abnormal points and rough difference points in a point cloud surface;
s2, carrying out setting error adjustment calculation based on plane constraint;
taking the placement angle error as an unknown parameter, converting a laser scanning coordinate system into an inertial platform reference coordinate system, combining an observed value in a geometric positioning model of an airborne laser radar system, establishing a calibration model, carrying out parameter calculation by utilizing a conditional variance with parameters, and then taking the placement eccentricity error as a parameter, and carrying out the same calculation to obtain the placement error;
s3, calculating step-by-step adjustment;
establishing and solving a plane equation with robust properties includes:
s1.1, setting a plane equation to be fitted as follows:
Figure QLYQS_1
（1）；
where a, b, c, d is an equation parameter, x, y, z represent the coordinates of a point;
the normal vector formed by the plane equation is considered as a unit normal vector, namely:
Figure QLYQS_2
（2）；
the distance from any point in space to the plane
Figure QLYQS_3
Expressed as:
Figure QLYQS_4
（3）；
wherein x is i 、y i 、z i Coordinates representing an arbitrary point;
s1.2, setting the best fit plane constraint condition
Figure QLYQS_5
The method comprises the following steps:
Figure QLYQS_6
（4）；
construction of Lagrangian auxiliary function
Figure QLYQS_7
：
Figure QLYQS_8
（5）；
In the method, in the process of the invention,
Figure QLYQS_9
is a parameter of the Lagrangian auxiliary function;
and d, obtaining a deviation, namely obtaining:
Figure QLYQS_10
（6）；
s1.3. rewriting formula (6) to:
Figure QLYQS_11
（7）；
wherein,,
Figure QLYQS_12
、/>
Figure QLYQS_13
、/>
Figure QLYQS_14
respectively x i 、y i 、z i Mean value of->
Figure QLYQS_15
；
Derivative a, b and c and let the derivative be 0, and obtaining:
Figure QLYQS_16
（8）；
in the method, in the process of the invention,
Figure QLYQS_17
the eccentricity error is set for each reference target point of the standard surface;
s1.4, constructing a eigenvalue equation:
Figure QLYQS_18
（9）；
obtaining the minimum eigenvalue of the coefficient matrix of the eigenvalue equation and the corresponding eigenvector thereof, namely obtaining a, b and c, and bringing the obtained a, b and c into the formula (3), thus obtaining d;
removing abnormal points and rough difference points in the point cloud surface comprises the following steps:
B1.1. calculating the distance between all points and the fitting plane according to a, b, c, d obtained in the step S1;
B1.2. calculating an error according to (10)
Figure QLYQS_19
：
Figure QLYQS_20
（10）；
Wherein n is the number of points,
Figure QLYQS_21
mean value of d, +.>
Figure QLYQS_22
；
B1.3. When meeting the requirements
Figure QLYQS_23
When (I)>
Figure QLYQS_24
Corresponding points are reserved, otherwise, the points are removed;
B1.4. recalculating plane parameters a, b, c, d by using the removed point cloud;
B1.5. repeating S2.1-S2.4 until all points are satisfied
Figure QLYQS_25
；
B1.5. Bringing a, b and c obtained in the step S2.5 into a formula (3), and obtaining d, wherein the best plane fitting equation is obtained;
s3:
taking the setting angle as a parameter, taking the translation amount as a known value, listing an equation for solving, and applying a Gaussian-Markov model by using a global least square method, wherein the solving principle comprises the following steps:
the global least squares method applies a gaussian-markov model as:
Figure QLYQS_26
；
in the middle of
Figure QLYQS_27
For placement error->
Figure QLYQS_28
For the coefficient matrix of n rows and m columns to be measured and calculated, < >>
Figure QLYQS_29
The error matrix exists in A, Y is an error vector to be calculated, and B is an error estimation parameter;
the step-by-step adjustment calculation step comprises the following steps:
s3.1, establishing a global least square method and applying a Gaussian-Markov model;
s3.2. pair amplification matrix
Figure QLYQS_30
Singular value decomposition is performed:
Figure QLYQS_31
；
wherein the method comprises the steps of
Figure QLYQS_33
，/>
Figure QLYQS_34
，/>
Figure QLYQS_35
、/>
Figure QLYQS_36
、/>
Figure QLYQS_37
、/>
Figure QLYQS_38
、/>
Figure QLYQS_39
、/>
Figure QLYQS_32
All are decomposed submatrices decomposed by singular values of the matrix;
s3.3. If
Figure QLYQS_40
Non-singular, get->
Figure QLYQS_41
，/>
Figure QLYQS_42
Is a linear regression of a sign, i.e. a straight line is made for a given number of points and the error minimum value of the points;
s3.4. precision assessment
Figure QLYQS_43
，/>
Figure QLYQS_44
I.e. standard deviation of placement error>
Figure QLYQS_45
In the range of 0.03-0.1, the accuracy of the placement error is reliable.
2. The gaussian-markov based airborne radar placement error interpolation correction method of claim 1, wherein converting the laser scanning coordinate system to the inertial platform reference coordinate system comprises:
s2.1. error prescriptionThe observations of a pass are symbolized as
Figure QLYQS_46
：/>
Figure QLYQS_47
；
Wherein:
Figure QLYQS_48
the scanning electrode diameter is; />
Figure QLYQS_49
Is the scan angle; />
Figure QLYQS_50
Is a roll angle; />
Figure QLYQS_51
Is a pitch angle; />
Figure QLYQS_52
Is the deflection angle; />
Figure QLYQS_53
Is the coordinates of the reference center in the WGS84 coordinate system;
the unknown parameters of the error equation are symbolized as
Figure QLYQS_54
：/>
Figure QLYQS_55
；
Wherein:
Figure QLYQS_56
for setting angle error->
Figure QLYQS_57
To accommodate eccentricity errors;
s2.2, converting the laser scanning coordinate system into an inertial platform reference coordinate system, wherein the method comprises the following steps of:
defining pitch angle inverse from laser scanning coordinate system to carrier coordinate system to inertial platform reference coordinate system
Figure QLYQS_58
Rotation is positive, side roll angle is reverse +.>
Figure QLYQS_59
Rotation is positive, course angle is reverse +.>
Figure QLYQS_60
Rotation is positive and +.>
Figure QLYQS_61
For the coordinates of the origin of the laser scanning coordinate system in the inertial platform reference coordinate system, it is assumed that the setting angles are positive, +.>
Figure QLYQS_62
Is the coordinate axis of the laser scanning coordinate system, +.>
Figure QLYQS_63
Is a coordinate axis of an inertial platform reference coordinate system;
s2.2.1. first winding
Figure QLYQS_64
Rotating Deltaroll, deltaroll being roll angle, & lt->
Figure QLYQS_65
Become->
Figure QLYQS_66
：
Figure QLYQS_67
（11）；
In the method, in the process of the invention,
Figure QLYQS_68
is +.>
Figure QLYQS_69
；
S2.2.2. winding
Figure QLYQS_70
Rotating Δpitch, which is pitch angle, and +.>
Figure QLYQS_71
Become->
Figure QLYQS_72
：
Figure QLYQS_73
（12）；
In the method, in the process of the invention,
Figure QLYQS_74
for +.>
Figure QLYQS_75
；
S2.2.3. winding
Figure QLYQS_76
Rotation delta yaw, delta yaw is the declination angle, +.>
Figure QLYQS_77
Become->
Figure QLYQS_78
：
Figure QLYQS_79
（13）；
In the method, in the process of the invention,
Figure QLYQS_80
is +.>
Figure QLYQS_81
；
S3.2.4. to sum up, formulae (11), (12), (13) can be obtained:
Figure QLYQS_82
（14）；
in the method, in the process of the invention,
Figure QLYQS_83
to simplify the matrix +.>
Figure QLYQS_84
。
3. The method for interpolation correction of placement errors of a gaussian-markov based airborne radar according to claim 2, wherein after converting the laser scanning coordinate system to the inertial platform reference coordinate system, the following steps are performed:
s2.3 plane equation of standard surface corresponding to calibration surface point cloud
Figure QLYQS_85
The following are provided:
Figure QLYQS_86
；
wherein,,
Figure QLYQS_87
；
Figure QLYQS_88
coordinate matrix for standard surface reference target point +.>
Figure QLYQS_89
For plane equationSetting a rotation error correction conversion matrix,>
Figure QLYQS_90
setting an eccentricity error correction conversion matrix for plane equation, < >>
Figure QLYQS_91
A coordinate matrix of the standard plane reference center in a WGS84 coordinate system;
Figure QLYQS_92
。
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